by Catalina Camia, USA TODAY

by Catalina Camia, USA TODAY

The selling of the bipartisan Senate immigration principles began in earnest Tuesday, as key GOP supporters John McCain and Marco Rubio fanned out on TV and radio to promote their proposal's merits.

Florida Sen. Rubio, a Tea Party favorite, appeared Tuesday afternoon on Rush Limbaugh's show, a day after the conservative talk show host criticized the bipartisan proposal as a form of amnesty.

"Things are often demagogued and described in a way that are not accurate," Rubio said on the syndicated radio program. "I think the more people are aware about what we're for and what we're not for, the more empowered we are ... to make a better argument for our position versus theirs."

A group of eight senators -- four Democrats and four Republicans -- on Monday announced they had reached agreement on four broad categories to be addressed in sweeping legislation to overhaul the nation's immigration system.

The principles include a path to citizenship, revamping the way immigrants come to the United States legally, boosting ways employers can verify the legal status of workers, and allowing more low-skill workers to come into the country. President Obama on Tuesday outlined his immigration proposal in a speech in Las Vegas.

McCain, R-Ariz., pushed back in CBS and MSNBC interviews on the idea that the proposal to create a pathway to citizenship for illegal immigrants already in the United States -- after border security is tightened and these migrants meet a strict set of conditions -- is not amnesty.

"Border enforcement and border security is a pre-requisite," McCain said on CBS This Morning. "And obviously that makes sense since we don't want to have a repeat again some years from now of another group of people coming to this country illegally."

McCain said a pathway to citizenship will be established for people already in the USA who have not committed crimes, pay fines and back taxes, and get in line behind those who have already applied legally for a green card.

"They will have to meet a lot of criteria," McCain said on CBS. "I hope that as more Americans see this proposal that they will understand that we cannot have forever 11 million people living in the shadows in this country."

Sen. Charles Schumer of New York, a leading Democrat in the bipartisan group, said Tuesday on MSNBC that there is nothing "easy" in the proposed path to citizenship. "There'll be some admission of wrongdoing. It is not amnesty in any sense of the word," Schumer said.

Rubio's appearance on Limbaugh's radio show could be critical. Limbaugh's syndicated show reaches millions of radio listeners, and the talk show host helps shape opinion among conservatives.

On Monday, as the senators unveiled their immigration principles, Limbaugh blasted the proposal and the idea that it is a way for Republicans to improve their standing with Latino voters.

"The Republican participation in this is taking place largely because they believe if they don't do it, they will never win the presidency again because they will never get Hispanic votes," Limbaugh said Monday.

Rubio said Tuesday that it is a "false argument" to characterize Republicans as anti-immigrant and anti-immigration. He stressed that legislation based on the Senate principles still needs to be written -- and he vowed he would not support the final product unless it contained border security and workplace enforcement ahead of a pathway to citizenship.

"If this bill does not have real triggers in there, if there is not language in this bill that guarantees that nothing else will happen unless these enforcement mechanisms are in place, I won't support it," Rubio said.

Rubio also challenged the president to work with the bipartisan group of senators, and not advance an immigration plan that is politically to the left of the framework that has been outlined.

"He can either decide that he wants to be part of a solution, or he can decide if he wants to be part of a political issue and try to trigger a bidding war," the Florida senator said, vowing not to get caught in a fight "to see who can come up with the most lenient path forward."

After the interview with Rubio, Limbaugh heaped praise on the senator as a "guy who does not fear talk radio."